Response of curved bridges subjected to vertical seismic pounding

Curved bridges exhibit complex dynamic behavior because plan curvature introduces torsion–bending coupling, which alters internal force distribution and support reactions compared to straight configurations. While seismic pounding has been widely investigated under horizontal ground motion, research on the influence of vertical excitation on pounding behavior in curved bridges is limited. This study examines pounding induced by vertical excitation in a two-span continuous curved bridge supported by rubber bearings using an analytical model based on a previous study. The girder is modeled as a simply supported curved Euler–Bernoulli beam, the pier as a vertically clamped elastic rod, and the bearing as a linear elastic spring. The inherently nonlinear contact problem is treated by distinguishing between in-contact and out-of-contact phases, each governed by linear elastic equations of motion derived from wave propagation theory. The method is validated against the straight bridge solution and demonstrates high accuracy when more than 50 vibration modes are included. A parametric study investigates the effects of curvature radius and excitation period. Results indicate that smaller radii significantly amplify pounding forces and produce more irregular impact patterns. Resonant vertical excitation leads to repeated separation, generating extremely high impact forces and excessive vertical displacements.